Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21458828 | C2 | semidirect |
| 2. #21448084 | C2 | semidirect |
| 3. #21447883 | C2 | semidirect |
| 4. #21447871 | C2 | semidirect |
| 5. #21447852 | C2 | semidirect |
| 6. #21447727 | C2 | semidirect |
| 7. #21447684 | C2 | semidirect |
| 8. C4×D976 | C2 | semidirect |
| 9. C61×#2249 | C2 | semidirect |
| 147. #2249 | D61 | semidirect |
| 184. C61 | #33970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458828 | 2 |
| #21448084 | 2 |
| #21447883 | 2 |
| #21447871 | 2 |
| #21447852 | 2 |
| #21447727 | 2 |
| #21447684 | 2 |
| C4×D976 | 2 |
| C61×#2249 | 2 |
| #33970 | 61 |